The processing and/or storage of an analog signal, such as an analog video signal, by a digital electronic system invariably requires conversion of the signal to a digital one by sampling the analog signal amplitude at periodic intervals and converting each sampled analog to a representative digital value. Depending on the desired degree of resolution, a large number of samples may be taken. Storage of a large number of signal samples (in the form of digital values) necessarily requires a large memory. Often the required memory capacity may not be available and, therefore, the signal samples must be compressed (i.e., reduced). Another advantage of compression may be found in data transmission. Transmitting a set of samples takes a finite time. Compressing the data can reduce transmission time, which is thus advantageous.
One approach to accomplishing data compression is to employ a least-squares type of regression analysis to fit the signal samples to a polynomial of the form a.sub.0 t.sup.0 +a.sub.1 t.sup.1 +a.sub.2 t.sup.2 . . . a.sub.n t.sup.n where n is an integer representing the degree of the polynomial, and t represents the time interval for a given sample. Rather than store or transmit the signal samples themselves, the coefficients a.sub.0,a.sub.1,a.sub.2 . . . a.sub.n are stored or transmitted instead. A desired signal sample at a corresponding time interval can be approximated from the polynomial.
The accuracy of such an approach is dependent on the value of n. By making n large, approximated signal sample values will correspond more closely to the true signal sample. However, making n too large (where n is on the order of the actual number of signal samples) defeats the entire purpose of compression altogether. Additionally, making n very large makes the least-squares regression analysis difficult to perform.
Thus, there is a need for a technique which allows for data compression while still maintaining high accuracy.